Can the Raspberry Pi do audio learning?
Typically what you probably would want to do is do the training on something other than a Raspberry Pi. I think for what you're wanting to accomplish with having a computer talk back to your parrot, you won't need anything too crazy with a bunch of GPU's - but I don't think you'll want to necessarily do the training on a Pi either. 

Here are some questions I have:


What are you going to plat back to the parrot? i.e. are you going to play it back random parrot sounds you found online or sounds that you've recorded? are you going to play it back what it just said? are you going to play it back a modification of what it just said?
Do you want it to respond to the parrot anytime the parrot speaks? Or when the parrot "says" something specific?


I think depending on the answers to those two questions, there are a couple of different paths that you could go down.

As for the hardware of the Raspberry Pi itself, I have never done any speech recognition with it, but I have done image recognition with it via the Movidius Neural Compute Stick which according to this Quora post, may be able to be used to offload some of the processing "relatively easily".

Here are some other links you may find valuable:


Tensorflow speech recognition: https://github.com/pannous/tensorflow-speech-recognition


The YouTube video that the above repo references: https://www.youtube.com/watch?v=u9FPqkuoEJ8

How to control a raspberry pi with your voice: http://www.techradar.com/how-to/how-to-control-the-raspberry-pi-with-your-voice
Voice recognition software setup on Raspberry Pi: https://diyhacking.com/best-voice-recognition-software-for-raspberry-pi/